Influence of Crystalline Nanoprecipitates on Shear-Band Propagation in Cu-Zr-Based Metallic Glasses

The interaction of shear bands with crystalline nanoprecipitates in Cu-Zr-based metallic glasses is investigated by a combination of high-resolution TEM imaging and molecular-dynamics computer simulations. Our results reveal different interaction mechanisms: Shear bands can dissolve precipitates, can wrap around crystalline obstacles, or can be blocked depending on the size and density of the precipitates. If the crystalline phase has a low yield strength, we also observe slip transfer through the precipitate. Based on the computational results and experimental findings, a qualitative mechanism map is proposed that categorizes the various processes as a function of the critical stress for dislocation nucleation, precipitate size, and distance.

Figure 1

An undeformed ${\mathrm{Zr}}_{53.8}{\mathrm{Cu}}_{31.6}{\mathrm{Ag}}_{7.0}{\mathrm{Al}}_{7.6}$ sample after annealing in a TEM bright-field image. An overview of the sample is shown in (a), with clearly visible crystalline precipitates. The inset (b) shows a magnified view, indicating the transition from globular to dendritic morphologies during precipitate growth. The different brightness of parts of one precipitate in (b) is most likely due to the different geometrical orientations of different parts of the same precipitate with respect to the incident electron beam. The strong black-white contrast change observed for some nanocrystals in (a) is most likely due to twinning.

Figure 2

TEM image of a shear band in a Zr-Cu-Ag-Al ribbon after deformation. The green arrows mark the positions of crystalline precipitates.

Figure 3

TEM and HRTEM images of a shear band. In the upper left corner, the electron transparent hole is visible, which stems from the sample preparation for TEM. (a), (b) Bright-field images of the same area, using a different tilt angle. The shear band appears as a white stripe, with part of it already cracked (bright white). (c) Dark-field image of the same area: The nanoprecipitates are visible and marked by circles. The crack stops at precipitate I; the shear band continues from there to precipitate II. (d) The power spectrum of precipitate II along the $⟨\overline{1}10⟩$ zone axis revealing superlattice reflections of the martensitic $B19^{\prime }$ structure. (e) HRTEM image of precipitate II, showing the shear band stopping at the precipitate. The contrast in (c) and (e) is enhanced to improve the visibility of the precipitates and the shear band.

Figure 4

Schematic simulation setup. The picture shows a cut through the three-dimensional simulation box in the $xz$ plane at $l/2$. A notch is inserted to control the origin of the shear band (yellow). The spherical precipitate is shown in blue. The box has open boundaries in the $x$ direction and is otherwise periodic. A constant strain rate is applied in the $z$ direction.

Figure 5

Snapshots of a simulation with a 30-nm CuZr precipitate. The shear band wraps around the precipitate and continues unhindered. The glass matrix is colored according to the atomic strain. The precipitate atoms are shown in blue if they appear in the $B2$ structure; no defects are visible. The left column shows a cut through the middle of the precipitate. On the right, all atoms with ${\eta }_i<0.3$ are deleted. A video version is provided in Video 1.

Figure 6

Comparison of the Orowan mechanism (a) with a shear band wrapping around precipitates (b). The slip plane is shown in gray, the precipitates in blue, the dislocation as a black line, and the shear band as a red plane. The precipitates can stop a dislocation because it must remain in a defined slip plane, while the shear band can temporarily leave its slip plane and continue unhindered afterwards.

Figure 7

Snapshots of a simulation with a 37.5-nm CuZr precipitate. The shear band is blocked by the precipitate, while a second shear band is immediately nucleated in another plane of high resolved shear stress. The glass matrix is colored according to the atomic strain. The precipitate atoms are shown in blue if they appear in the $B2$ structure; no defects are visible. The left column shows a cut through the middle of the precipitate. On the right, all atoms with ${\eta }_i<0.3$ are deleted. A video version is provided in Video 2.

Figure 8

Influence of the precipitate size and distance on the mechanism. (a) Explanation of the parameter $l$, distance of the precipitates, and $A$, the area of a cut through the precipitate. (b) shows a contour plot of the empirical geometry factor $\mathrm{\Lambda }=A/l$. The dashed line shows the critical value of $\mathrm{\Lambda }$ for a transition from the wrapping to the blocking mechanism. Data points are MD simulations. The data points at $l=0\mathrm{nm}$ are infinite cylinders along the $y$ axis, representing the case of overlapping spheres with infinitesimally small distances between their centers.

Figure 9

Stress-strain curves of samples which exhibit the wrapping or blocking mechanisms. The arrows indicate when the shear band hits the precipitate.

Figure 10

Mechanical dissolution of a 3-nm copper particle in a shear band. The gray-scale color coding shows atomic strain ${\eta }_i$ from 0.0 (black) to 1.0 (white). The precipitate is shown in color: Light blue atoms are in the fcc structure, green atoms are in a stacking fault, and dark blue atoms are disordered. The arrows indicate the shear direction. (a) shows a cut through the middle of the nanoprecipitate, while (b) shows only the atoms that initially belonged to the nanoprecipitate.

Figure 11

Stress-strain curves for the composites with fcc copper precipitates and for a 10-nm copper nanowire. (a) Curves from simulations with the Mendelev potential. The copper precipitates do not deform plastically and show similar behavior to the CuZr precipitates discussed earlier. The curve of the copper nanowire explains this: The yield stress, and therefore the critical shear stress, is higher than the highest resolved shear stress in the steady state in the composite. To be able to compare the tensile stress in the composite with the shear stress in the nanowire, the tensile stress axis is scaled with a factor of 0.5 corresponding to the Schmid factor for the plane of highest resolved shear stress. (b) Curves from simulations with the Ward potential. Now the critical stress for heterogeneous dislocation nucleation is lower than the steady-state stress in the composite, and the precipitate deforms plastically. (c) The simulation setup for the nanowire. The wire is sheared in the [110] direction of the fcc crystal structure on the (111) plane. The red atoms are fixed, and the atoms on the top are shifted with a constant velocity to shear the nanowire.

Figure 12

Snapshots of a simulation with a 30-nm copper precipitate. This simulation uses the Ward potential, in which the critical stress for dislocation nucleation is realistic. As the precipitate is sufficiently soft, the shear band can cut through it. The glass matrix is colored according to the atomic strain (the same scale as Figs. 5 and 7). Defects in the fcc crystal structure are colored according to the legend. The left column shows a cut through the middle of the precipitate. On the right, all atoms with ${\eta }_i<0.3$ and all fcc-coordinated atoms are deleted. A video version is provided in Video 3.

Figure 13

Projection of the forces and stresses acting around the precipitate (blue circle) onto the $xz$ plane. Shear bands are shown as hatched areas, where yellow signifies the arriving shear band, green the path for wrapping, and red the site for the nucleation of a new shear band.

Figure 14

Schematic view of different mechanisms for the interaction of a shear band with a crystalline precipitate. With increasing precipitate sizes, the dissolution of the precipitate is first replaced by the wrapping mechanism. Depending on the critical stress for dislocation nucleation, wrapping is replaced by blocking or cutting. Wrapping can be favored by increasing the precipitate distance.

Figure 15

Generalized stacking-fault energies (top) and the resulting shear stresses (bottom) for fcc copper. The DFT values for the stress curve are from Ogata, Li, and Yip [58], and the corresponding stacking-fault energies are approximated by using a numerical integration of the stress data.